Physics-Based Animation

Breannan Smith, Danny Kaufman, Etienne Vouga, Rasmus Tamstorf, Eitan Grinspun

Resolving simultaneous impacts is an open and significant problem in collision response modeling. Existing algorithms in this domain fail to fulfill at least one of five physical desiderata. To address this we present a simple generalized impact model motivated by both the successes and pitfalls of two popular approaches: pair-wise propagation and linear complementarity models. Our algorithm is the first to satisfy all identified desiderata, including simultaneously guaranteeing symmetry preservation, kinetic energy conservation, and allowing break-away. Furthermore, we address the associated problem of inelastic collapse, proposing a complementary generalized restitution model that eliminates this source of nontermination. We then consider the application of our models to the synchronous time-integration of large-scale assemblies of impacting rigid bodies. To enable such simulations we formulate a consistent frictional impact model that continues to satisfy the desiderata. Finally, we validate our proposed algorithm by correctly capturing the observed characteristics of physical experiments including the phenomenon of extended patterns in vertically oscillated granular materials.

Reflections on Simultaneous Impact

Jernej Barbic, Funshing Sin, Eitan Grinspun

We present an interactive animation editor for complex deformable object animations. Given an existing animation, the artist directly manipulates the deformable body at any time frame, and the surrounding animation immediately adjusts in response. The automatic adjustments are designed to respect physics, preserve detail in both the input motion and geometry, respect prescribed bilateral contact constraints, and controllably and smoothly decay in spacetime. While the utility of interactive editing for rigid body and articulated figure animations is widely recognized, a corresponding approach to deformable bodies has not been technically feasible before. We achieve interactive rates by combining spacetime model reduction, rotation-strain coordinate warping, linearized elasticity, and direct manipulation. This direct editing tool can serve the final stages of animation production, which often call for detailed, direct adjustments that are otherwise tedious to realize by re-simulation or frame-by-frame editing.

Interactive Editing of Deformable Simulations

Christopher Batty, Andres Uribe, Basile Audoly, Eitan Grinspun

We present the first reduced-dimensional technique to simulate the dynamics of thin sheets of viscous incompressible liquid in three dimensions. Beginning from a discrete Lagrangian model for elastic thin shells, we apply the Stokes-Rayleigh analogy to derive a simple yet consistent model for viscous forces. We incorporate nonlinear surface tension forces with a formulation based on minimizing discrete surface area, and preserve the quality of triangular mesh elements through local remeshing operations. Simultaneously, we track and evolve the thickness of each triangle to exactly conserve liquid volume. This approach enables the simulation of extremely thin sheets of viscous liquids, which are difficult to animate with existing volumetric approaches. We demonstrate our method with examples of several characteristic viscous sheet behaviors, including stretching, buckling, sagging, and wrinkling.

Discrete Viscous Sheets

Changsoo Je, Min Tang, Youngeun Lee, Minkyoung Lee, Young J. Kim

We present a real-time algorithm that finds the Penetration Depth (PD) between general polygonal models based on iterative and local optimization techniques. Given an in-collision configuration of an object in configuration space, we find an initial collision-free configuration using several methods such as centroid difference, maximally clear configuration, motion coherence, random configuration, and sampling-based search. We project this configuration on to a local contact space using a variant of continuous collision detection algorithm and construct a linear convex cone around the projected configuration. We then formulate a new projection of the in-collision configuration onto the convex cone as a Linear Complementarity Problem (LCP), which we solve using a type of Gauss-Seidel iterative algorithm. We repeat this procedure until a locally optimal PD is obtained. Our algorithm can process complicated models consisting of tens of thousands triangles at interactive rates.

PolyDepth: Real-Time Penetration Depth Computation using Iterative Contact-Space Projection

Ondrej Stava, Juraj Vanek, Bedrich Benes, Nathan Carr, Radomir Mech

3D printing is a rapidly maturing area that has shown great progress over the past couple of years. It is now possible to produce 3D printed objects with exceptionally high fidelity and precision. However, while the quality of 3D printing has gone up, both the time to print and material costs have remained high. Moreover, there is no guarantee that a printed model is structurally sound. Many times, the printed product does not survive cleaning, transportation, or handling, or it even collapses under its own weight. We present a system that addresses this issue by providing automatic detection and correction of the problematic cases. The structural problems are detected by combining a lightweight structure analysis solver with 3D medial axis approximations. After areas with high structural stress are found, the model is corrected by combining three approaches: hollowing, thickening, and strut insertion. This detection and correction repeats until all problematic cases are corrected. Our process is designed to create a model that is visually similar to the original model, while possessing greater structural integrity

Stress Relief: Improving Structural Strength of 3D Printable Objects

Steffen Weissman, Ulrich Pinkall

We show that the motion of rigid bodies under water can be realistically simulated by replacing the usual inertia tensor and scalar mass by the so-called Kirchhoff tensor. This allows us to model fluid-body interaction without simulating the surrounding fluid at all. We explain some of the phenomena that arise and compare our results against real experiments. It turns out that many real scenarios (sinking bodies, balloons) can be matched using a single, hand-tuned scaling parameter. We describe how to integrate our method into an existing physics engine, which makes underwater rigid body dynamics run in real time.

Underwater Rigid Body Dynamics

Tobias Pfaff, Nils Thuerey, Markus Gross

Buoyant turbulent smoke plumes with a sharp smoke-air interface, such as volcanic plumes, are notoriously hard to simulate. The surface clearly shows small-scale turbulent structures which are costly to resolve. In addition, the turbulence onset is directly visible at the interface, and is not captured by commonly used turbulence models. We present a novel approach that employs a triangle mesh as a high-resolution surface representation combined with a coarse Eulerian solver. On the mesh, we solve the interfacial vortex sheet equations, which allows us to accurately simulate buoyancy induced turbulence. For complex boundary conditions we propose an orthogonal turbulence model that handles vortices caused by obstacle interaction. In addition, we demonstrate a re-sampling scheme to remove surfaces that are hidden inside the bulk volume. In this way we are able to achieve highly detailed simulations of turbulent plumes efficiently.

Lagrangian Vortex Sheets for Animating Fluids

Hagit Schechter, Robert Bridson

We propose a new ghost fluid approach for free surface and solid boundary conditions in Smoothed Particle Hydrodynamics (SPH) liquid simulations. Prior methods either suffer from a spurious numerical surface tension artifact or drift away from the mass conservation constraint, and do not capture realistic cohesion of liquid to solids. Our Ghost SPH scheme resolves this with a new particle sampling algorithm to create a narrow layer of ghost particles in the surrounding air and solid, with careful extrapolation and treatment of fluid variables to reflect the boundary conditions. We also provide a new, simpler form of artificial viscosity based on XSPH. Examples demonstrate how the new approach captures real liquid behaviour previously unattainable by SPH with very little extra cost.

Ghost SPH for Animating Water

Eder Miguel, Derek Bradley, Bernhard Thomaszewski, Bernd Bickel, Wojciech Matusik, Miguel Otaduy, Steve Marschner

Progress in cloth simulation for computer animation and apparel design has led to a multitude of deformation models, each with its own way of relating geometry, deformation, and forces. As simulators improve, differences between these models become more important, but it is difficult to choose a model and a set of parameters to match a given real material simply by looking at simulation results. This paper provides measurement and fitting methods that allow nonlinear models to be fit to the observed deformation of a particular cloth sample. Unlike standard textile testing, our system measures complex 3D deformations of a sheet of cloth, not just one-dimensional force–displacement curves, so it works under a wider range of deformation conditions. The fitted models are then evaluated by comparison to measured deformations with motions very different from those used for fitting.

Data-Driven Estimation of Cloth Simulation Models

Tyson Brochu, Essex Edwards, Robert Bridson

Continuous collision detection (CCD) between deforming triangle mesh elements in 3D is a critical tool for many applications. The standard method involving a cubic polynomial solver is vulnerable to rounding error, requiring the use of ad hoc tolerances, and nevertheless is particularly fragile in (near-)planar cases. Even with per-simulation tuning, it may still cause problems by missing collisions or erroneously flagging non-collisions. We present a geometrically exact alternative guaranteed to produce the correct Boolean result (significant collision or not) as if calculated with exact arithmetic, even in degenerate scenarios. Our critical insight is that only the parity of the number of collisions is needed for robust simulation, and this parity can be calculated with simpler non-constructive predicates. In essence we analyze the roots of the nonlinear system of equations defining CCD through careful consideration of the boundary of the parameter domain. The use of new conservative culling and interval filters allows typical simulations to run as fast as with the non-robust version, but without need for tuning or worries about failure cases even in geometrically degenerate scenarios. We demonstrate the effectiveness of geometrically exact detection with a novel adaptive cloth simulation, the first to guarantee to remain intersection-free despite frequent curvature-driven remeshing.

Efficient Geometrically Exact Continuous Collision Detection